The Average Symmetry Index of Minerals Co-Varies with Their Hydrogen Content, Rarity, and Paragenetic Mode

Abstract

Variations in the Dolivo-Dobrovol’sky symmetry index for minerals through time reveal several factors that influence the emergence of crystalline symmetry in natural processes. Of special interest in this regard are the numerous paragenetic modes—different processes of mineral genesis that reflect changes in physical, chemical, and ultimately biological environments that foster the emergence of new mineral species. Here, we consider the roles of hydrogen content, rarity, formation temperature and pressure, and age on the average symmetry of minerals from 57 different modes of formation (i.e., paragenetic modes). We find four significant trends in the average mineral symmetry index for all minerals in each paragenetic mode: specifically, this average index is (1) lower for minerals with greater hydrogen content; (2) greater for minerals formed at higher pressure; (3) lower for minerals of greater rarity; and (4) greater for older paragenetic modes. These findings elucidate some of the intricate relationships among paragenetic modes, average mineral attributes, and the Dolivo-Dobrovol’sky symmetry index, providing insights into the geological processes governing mineral formation.

Crystal Structure Complexity and Approximate Limits of Possible Crystal Structures Based on Symmetry-Normalized Volumes

“…There appears to be a tentative preference for cubic symmetry among the high V sym phases and a preference for monoclinic phases at small Z and close to the high-density limit (see Table 2 ). The small number of triclinic phases is likely a bias from the limited number of phases and the exclusion of compounds with H-bonds [ 24 , 25 ]. An apparent preference for high crystal symmetry at high Z is noteworthy and deserves future study.…”

“…V sym of H-bearing phases is expected to show a systematic shift toward lower values compared to non-H-bearing phases, which is indirectly expressed in the apparent negative crystal radius of H + [ 19 ]. I cmplx is expected to be shifted to larger values [ 25 ].…”